First, from now on, don't force him to believe in Buddhism and be a vegetarian, which was caused by your previous life. Don't push him, the more you push him, the farther away he is from you.
Second, I'm afraid it's hard for you to do it, but it may be the only way to keep him. That is, when you start to learn Buddhism, if you practice better than him, you can change your son's heart. I've been a vegetarian for three years, and now I'm doing well. I don't want to become a monk. I think as long as there is a sincere heart, it is the same everywhere. I learn Buddhism in a different way from your son. Learning Buddhism should start from the heart, put filial piety first, learn the compassion and wisdom of Buddhism, let go of persistence and separation, and keep yourself and others away from troubles. This is the Buddha's great wish-to save all beings. If learning Buddhism makes people around you worry, hate and even want to die, it is the wrong way. Your son learned Buddhism in the wrong way, but he won't listen to you now. Only you can change him with practical actions.
Third, how to change him with actions? This can't be done in a day or two. First of all, you should learn the ten good and five commandments and do better than your son. If he lives together, he can't have no feelings. It is important to be sincere in worshipping Buddha, not to have a red forehead. Sincerity depends not on appearance, but on sincerity. Your son's wisdom has not been opened yet. Be sure to read Heart Sutra 2 1 to 49 times every day. Before reading, you should say: Please be merciful, Guanyin Bodhisattva, and help my son (name) to open his wisdom.
If you do this first, it will have an effect.